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Lecture 3 Spring 2003
NUCLEOSYNTHESIS
A reasonable starting point for isotope geochemistry is a determination of the abundances of t h e naturally occurring nuclides. Indeed, this was the first task of isotope geochemists (though those engaged in this work would have referred to themselves simply as physicists). We noted this began with Thomson, who built the first mass spectrometer and discovered Ne consisted of 2 isotopes (actually, it consists of three, but one of them, 21 Ne is very much less abundant than the other two, and Thomson’s primitive instrument did not detect it). Having determined the abundances of nu- clides, it is natural to ask what accounts for this distribution, and even more fundamentally, what processes produced the elements. This process is known as nucleosynthesis. The abundances of naturally occurring nuclides is now reasonably, though perhaps not perfectly, known. We also have what appears to be a reasonably successful theory of nucleosynthesis. Physi- cists, like all scientists, are attracted to simple theories. Not surprisingly then, the first ideas about nucleosynthesis attempted to explain the origin of the elements by single processes. Generally, these were thought to occur at the time of the Big Bang. None of these theories was successful. It was re- ally the astronomers, accustomed to dealing with more complex phenomena than physicists, who suc- cessfully produced a theory of nucleosynthesis that involved a number of processes. Today, isotope geochemists continue to be involved in refining these ideas by examining and attempting to explain isotopic variations occurring in some meteorites. The origin of the elements is an astronomical question, perhaps even more a cosmological one. To understand how the elements formed we need to understand a few astronomical observations and con- cepts. The universe began some 10 to 20 Ga ago with the Big Bang. Since then the universe has been expanding, cooling, and evolving. This hypothesis follows from two observations: the relationship between red-shift and distance and the cosmic background radiation, particularly the former. This cosmology provides two possibilities for formation of the elements: (1) they were formed in the Big Bang itself, or (2) they were subsequently produced. In actuality, both are involved. Our present understanding of nucleosynthesis comes from three sorts of observations: (1) the abun- dance of isotopes and elements in the Earth, Solar System, and cosmos (spectral observations of stars), (2) experiments on nuclear reactions that determine what reactions are possible (or probable) under given conditions, and (3) inferences about possible sites of nucleosynthesis and about the conditions that would prevail in those sites. The abundances of the elements in the Solar System are shown in Figure 3.1. Various hints came from all three of the above observations. For example, it was noted that the most abundant nuclide of a given set of stable isobars tended to be the most neutron-rich one. We now understand this to be a result of shielding from b-decay (see the discussion of the r-process). Another key piece of evidence regarding formation of the elements comes from looking back into t h e history of the cosmos. Astronomy is a bit like geology in that just as we learn about the evolution of the Earth by examining old rocks, we can learn about the evolution of the cosmos by looking at old stars. It turns out that old stars (such old stars are most abundant in the globular clusters outside t h e main disk of the Milky Way) are considerably poorer in heavy elements than are young stars. This suggests much of the heavy element inventory of the galaxy has been produced since these stars formed (some 10 Ga ago). On the other hand, they seem to have about the same He/H ratio as young stars. Indeed 4 He seems to have an abundance of 24-28% in all stars. Another key observation was the identification of Technetium emissions in the spectra of some stars. Since the most stable isotope of this element has a half-life of about 100,000 years, it must have been synthesized in the stars. Thus the observational evidence suggests (1) H and He are everywhere uniform implying their crea- tion and fixing of the He/H ratio in the Big Bang and (2) subsequent creation of heavier elements (heavier than Li, as we shall see) by subsequent processes. As we mentioned, early attempts (~1930–1950) to understand nucleosynthesis focused on single mechanisms. Failure to find a single mechanism that could explain the observed abundance of nuclides, even under varying conditions, led to the present view that relies on a number of mechanisms
Lecture 3 Spring 2003
operating in different environments and at different times for creation of the elements in their observed abundances. This view, often called the polygenetic hypothesis, is based mainly on t h e work of Burbidge, Burbidge, Fowler and Hoyle. Their classic paper summarizing the theory, "Synthesis of the Elements in Stars" was published in Reviews of Modern Physics in 1956. Interestingly, the abundance of trace elements and their isotopic compositions, were perhaps the most critical observations in development of the theory. An objection to this polygenetic scenario was t h e apparent uniformity of the isotopic composition of the elements. But variations in the isotopic composition have now been demonstrated for many elements in some meteorites. The isotopic compositions of other elements, such as oxygen and the rare gases, vary between classes of almost a l l meteorites. Furthermore, there are quite significant compositional variations in heavier elements among stars. These observations provide strong support for this theory. To briefly summarize it, the polygenetic hypothesis proposes four phases of nucleosynthesis. Cos- mological nucleosynthesis occurred shortly after the universe began and is responsible for the cosmic inventory of H and He, and some of the Li. Helium is the main product of nucleosynthesis in the inte- riors of normal, or “main sequence” stars. The lighter elements, up to and including Si, but excluding Li and Be, and a fraction of the heavier elements may be synthesized in the interiors of larger stars dur- ing the final stages of their evolution ( stellar nucleosynthesis ). The synthesis of the remaining ele- ments occurs as large stars exhaust the nuclear fuel in their interiors and explode in nature’s grandest spectacle, the supernova ( explosive nucleosynthesis ). Finally, Li and Be are continually produced in interstellar space by interaction of cosmic rays with matter ( galactic nucleosynthesis ). In the following sections, we examine these nucleosynthetic processes as presently understood.
COSMOLOGICAL NUCLEOSYNTHESIS
Immediately after the Big Bang, the universe was too hot for any matter to exist. But after a second or so, it had cooled to 10 1 0 K so that a few protons and neutrons existed in an equilibrium dictated by the following reactions: Figure 3.1. Solar system abundance of the elements relative to silicon as a function of atomic number.
Lecture 3 Spring 2003
hot; K and M stars are small, cool, and (comparatively speaking) dark. Stars on the main sequence produce energy by ‘hydrogen burning', fusion of hydrogen to produce helium. Since the rate at which these reactions occur depends on temperature and density, hot, massive stars release more energy than smaller ones. As a result, they exhaust t h e hydrogen in their cores much more rapidly. Thus there is an inverse re- lationship between the lifetime of a star, or at least the time it spends on the main sequence, and its mass. The most massive stars, up to 100 solar masses, have life expectancies of only about 106 years, whereas small stars, as small as 0. solar masses, remain on the main sequence more than 1010 years. The two most important exceptions to the main sequence stars, the red giants and the white dwarfs, represent stars that have burned all the H fuel in their cores and have moved on in the evolu- tionary sequence. When the H in the core is converted to He, it generally cannot be replenished because the density differ- ence prevents convection between the core and out layers, which are still H rich. The interior part of the core collapses un- der gravity. With enough collapse, the layer immediately above the He core will begin to 'burn' H again, which again stabilizes the star. The core, however, continues to collapse until T and P are great enough for He burning to begin. At the same time, and for reasons not fully understood, t h e exterior expands and cools, resulting in a red giant , a star that is over-luminous relative to main sequence stars of the same color. When the Sun reaches this phase, in perhaps another 5 Ga, it will expand to the Earth's orbit. A star will remain in the red giant phase for of the order of 106 –10^8 years. During this time, radiation pressure results in a greatly enhanced solar wind, of the order of 10 -6^ to 10 - (^7) , or even 10 -4, solar masses per years (the Sun's solar wind is 10 -14 (^) solar masses; i.e., in its entire lifetime, the Sun will blow off 1/10,000 of its mass through solar wind). The fate of stars after the red giant phase (when the He in the core is exhausted) depends on their mass. Nuclear reactions in small stars cease and they simply contract, their exteriors heating up as they do so, to become white dwarfs. The energy released is that produced by previous nuclear reac- tions and released gravitational potential energy. This is the likely fate of the Sun. White Dwarfs are underluminous relative to stars of similar color on the main sequence. They can be thought of as little more than glowing ashes. Unless they blow off sufficient mass during the red giant phase, stars larger than 1.5 solar masses die explosively, in supernovae. (Novae are entirely different events which occur in binary systems when mass from a main sequence star is pull by gravity onto a white dwarf companion). Supernovae are incredibly energetic events. The energy released by a supernova can exceed that released by an entire galaxy (which, it will be recalled, consists of on the order of 109 stars) for a period of days or weeks! a
b T-Tauri
Stars
Sun
SuperGiants
Red Giants
White Dwarfs
Blue White Yellow Red
O B A F G K M
Surface Temperature (10^3 K)
Spectral Class
Figure 3.2. The Hertzsprung-Russell diagram of t h e relationship between luminosity and surface tem- perature. Arrows show evolutionary path for a star t h e size of the Sun in pre- (a) and post- (b) main sequence phases.
Lecture 3 Spring 2003
Nucleosynthesis in Stellar Interiors
Hydrogen, Helium, and Carbon Burning in Main Sequence and Red Giant Stars
For quite some time after the Big Bang, the universe was a more or less homogeneous, hot gas. More or less turns out to be critical wording. Inevitably (according to fluid dynamics), inhomogeneities in the gas developed. These inhomogeneities enlarged in a sort of runaway process of gravitational a t - traction and collapse. Thus were formed protogalaxies, thought to date to about 0.5-1.0 Ga after t h e big bang. Instabilities within the protogalaxies collapsed into stars. Once this collapse proceeds to the point where density reaches 6 g/cm and temperature reaches 10 to 20 million K, nucleosynthesis begins in the interior of stars, by hydrogen burning , or the pp process. There are three variants, PP I:
1 H + 1 H Æ 2 H +b+ + n; 2 H + 1 H Æ 3 He + g; and 3 He + 3 He Æ 4 He + 21 H + g
PP II:
3 He + 4 He Æ 7 Be; 7 Be Æ b– + 7 Li + n; 7 Li + 1 H Æ 24 He
and PP III:
7 Be + 1 H Æ 8 B + g; 8 B Æ b+ + 8 Be + n; 8 Be Æ 24 He
Which of these reactions dominates depends on temperature. The net result of all three reactions is the production of 4 He and the consumption of H as well as Li and B. All main sequence stars produce He, yet over the history of the cosmos, this has had little impact on the H/He ratio of the universe. This in part reflects the observation that for small mass stars, the He produced remains hidden in their interiors or their white dwarf remnants and for large mass stars, later reactions consume the He produced in the main sequence stage. Once some carbon had been produced by the first generation of stars and supernovae, second and sub- sequent generation stars with masses greater than about 1.1 solar masses produced He by another process as well, the CNO cycle :
12 C(p,g) 13 N(b+,g) 13 C(p,g) 14 N(p,g) 15 O(b+,n) 15 N(p,a) 12 C‡
It was subsequently realized that this reaction cycle is just part of a larger reaction cycle, which is i l - lustrated in Figure 3.3. Since the process is cyclic, the net effect is consumption of 4 protons and two positrons to produce a neutrino, some energy, and a 4 He nucleus. Thus to a first approximation, carbon ‡ (^) Here we are using a notation commonly used in nuclear physics. The reaction:
12 C(p,g) 13 N
(p,g)
13 C
(a,p) (p,g)
14 N 17 O 18 F
13 N 15 O 17 F
(p,a) (p,g)
(p,a)
12 C 15 N 16 O 18 O^ (p,g)^19 F (p,g) 20 Ne
(p,
g)
(e+,
n)
(p,
g)
(e+,
n)
(e+,
n)
(p,
g)
(e+,
n)
I II III
Figure 3.3. Illustration of the CNO cycle, which operates in larger second and later generation stars.
Lecture 3 Spring 2003
itational collapse. Massive stars, those greater than about 1.5 solar masses, however, undergo further collapse and further evolution. Evolution now proceeds at an exponentially increasing pace (Figure 3.4), and these phases are poorly understood. But if temperatures reach 600 million K and densities 5 x 105 g/cc, carbon burning becomes possible:
1 2C + 1 2C Æ 2 0Ne + 4 He + g
The carbon burning phase marks a critical juncture in stellar evolution. As we mentioned, low mass stars never reach this point. Intermediate mass stars, those with 4-8 solar masses can be catastrophically disrupted by the ignition of carbon burning. But in large stars, the sequence of production of heavier and heavier nuclei continues. After carbon burning, there is an episode called Ne burning, in which 20 Ne is decomposed by (g,a) reactions. The a's are consumed by those nuclei present, including 20 Ne. The next phase is oxygen burning, which involves reactions such as:
1 6O+ 1 6OÆ 2 8Si + 4 He + g and 1 2C + 1 6O Æ 2 4Mg + 4 He + g
A number of other less abundant nuclei, including Na, Al, P, S and K are also synthesized at this time, and in the subsequent process, Ne burning. During the final stages of evolution of massive stars, a significant fraction of the energy released is carried off by neutrinos created by electron-positron annihilations in the core of the star. If the star is sufficiently oxygen-poor that its outer shells are reasonably transparent, the outer shell of the red giant may collapse during last few 104 years of evolution to form a blue giant.
The e-process
Eventually, a new core consisting mainly of 28 Si is produced. At temperatures near 109 K and densi- ties above 107 g/cc a process known as silicon burning , or the e process , (for equilibrium) begins, and lasts for days or less, again depending on the mass of the star. These are reactions of the type:
2 8Si + g ® 2 4Ne + 4 He
2 8Si + 4 He ® 3 2S + g
3 2S + 1 4He ® 3 6Ar + g
While these reactions can go either direction, there is some tendency for the build up of heavier nuclei with masses 32, 36, 40, 44, 48, 52 and 56. Partly as a result of the e-process, these nuclei are unusually abundant in nature. In addition, because of a variety of nuclei produced during C and Si burning phases, other reactions are possible, synthesizing a number of minor nuclei. The star is now a cosmic onion of sorts (Figure 3.5), consisting of a series of shells of successively heavier nuclei and a core of Fe. Though temperature increases toward the interior of the star, the structure is stabilized with respective to convec- tion and mixing because the each shell is denser than the one overlying it. Fe-group elements may also be syn- thesized by the e-process in Type I su- pernovae. Type I supernovae occur when white dwarfs of intermediate Figure 3.5. Schematic diagram of stellar structure at t h e onset of the supernova stage. Nuclear burning processes are illustrated for each stage.
Lecture 3 Spring 2003
mass (3-10 solar masses) stars in binary systems accrete material from their companion. When their cores reach the Chandrasekhar limit, C burning is ini- tiated and the star explodes. This theoretical scenario has been confirmed in recent years by space based optical, gamma-ray, and x-ray observations of supernovae, such as the Chandra X-ray observatory image in Figure 3.6.
The s-process
In second and later generation stars containing heavy elements, yet another nucleosynthetic process can operate. This is the slow neutron capture or s- process. It is so called because the rate of capture of neutrons is slow, compared to the r-process , which we will discuss below. It operates mainly in the red giant phase (as evidenced by t h e existence of 99 Tc and enhanced abundances of several s-process ele- ments) where neutrons are produced by reactions such as:
1 3C + 4 He Æ 16 O + 1 n
22 Ne + 4 He Æ 25 Mg + 1 n
17 O + 4 He Æ 20 Ne + 1 n
(but even H burning produces neutrons; one consequence of this is that fusion reactors will not be completely free of radiation hazards). These neutrons are captured by nuclei to produce successively heavier elements. The principle difference between the r and s process is the rate of capture relative to the decay of unstable isotopes. In the s-process, a nucleus may only capture a neutron every thousand years or so. If the newly produced nucleus is not stable, it will decay before another neutron is captured. As a result, instabilities cannot be bridged as they can in the r-process discussed below. In the s-process, the rate of formation of stable species is given by
d [A]
dt
= ƒ[A – 1]s A–
where [A] is the abundance of a nuclide with mass number A, ƒ is a function of neutron flux and neutron energies, and s is the neutron-capture cross section. Note that a nuclide with one less proton might contribute to this build up of nuclide A, provided that the isobar of A with one more neutron is not sta- ble. The rate of consumption by neutron capture is:
d[A]
dt
= –ƒ[A]sA
From these relations we can deduce that the ratio creation of two nuclides with mass numbers A and A-1 will be proportional to the ratio of their capture cross sections: Figure 3.6. Chandra X-ray image of the supernova remnant Cassiopeia A (Cas A). The red, green, and blue regions in this Chandra X-ray image of the supernova remnant Cassiopeia A show where the intensity of low, medium, and high energy X-rays, respectively, is greatest. The red material on the left outer edge is enriched in iron, whereas the bright greenish white region on the lower left is enriched in silicon and sulfur. In the blue region on the right edge, low and medium energy X-rays have been filtered out by a cloud of dust and gas in the remnant.
Lecture 3 Spring 2003
lapse of this stellar core, which would have a radius similar to that of the Earth’s before collapse, to a radius of 100 km or so. This occurs in a few tenths of a second. As matter in the center of the core is compressed beyond the density of nuclear matter (3 ¥ 1014 g/cc), it rebounds, sending a massive shock wave back out less than a second after the collapse begins. As the shock wave travels outward through the core, the temperature increase resulting from the compression produces a break down of nuclei by photodisintegration, e.g.: This results in the production of a large number of free neutrons (and protons), which is the important result. The neutrons are captured by those nuclei that manage to survive this hell. In the core itself, the reactions are endothermic, and thermal energy cannot overcome the gravitational energy, so i t continues to collapse. If the original mass of the star is > 4 solar masses, the result is a neutron star, in which all matter is compressed into neutrons. Supernova remnants of masses greater than 8 solar masses can collapse to produce a singularity, where density is infinite. A supernova remnant having the mass of the sun would form a neutron star of only 15 km radius. A singularity of similar mass would be surrounded by a black hole, a region whose gravity field is so intense even light cannot es- cape, with a radius of 3 km. Another important effect is the creation of huge numbers of neutrinos by positron-electron annihila- tions, which in turn had “condensed” as pairs from gamma rays. The energy carried away by neutrino leaving the supernova exceeds the kinetic energy of the explosion by a factor of several hundred, and exceeds the visible radiation by a factor of some 30,000. The neutrinos leave the core at nearly t h e speed of light. Though neutrinos, which travel at nearly the speed of light, interact with matter very weakly, the density of the core is such that their departure is delayed slightly. Nevertheless, they travel faster than the shock wave and are delayed less than electromagnetic radiation. Thus neutrinos from the 1987A supernova arrived at Earth (some 160,000 years after the event) a few hours before the supernova became visible. The shock wave eventually reaches the surface of the core, and the outer part of the star is blown apart in an explosion of unimaginable violence. Amidst the destruction new nucleosynthetic processes are occurring. This first of these is the r process (rapid neutron capture), and is the principle mechanism for building up the heavier nuclei. In the r-process, the rate at which nuclei with mass number A+1 are created by capture of a neutron by nuclei with mass number A can be expressed simply as:
NAsAƒ
where NA is the number of nuclei with mass number A, s is the neutron capture cross section and ƒ is t h e neutron flux. If the product nuclide is unstable, it will decay at a rate given by lNA+1. It will also capture neutrons itself, so the total destruction rate is given by
lNA+1+ NA+1sA+1ƒ
An equilibrium distribution occurs when nuclei are created at the same rate as they are destroyed, i.e.:
NAsAF = lNA+1+ NA+1sA+1ƒ
Thus the equilibrium ratio of two nuclides A and A+1 is:
NA/NA+1 = (l+ sA+1F)/sAƒ
Eventually, some nuclei capture enough neutrons that they are not stable even for short periods (in terms of the above equation, l becomes large, hence NA/NA+1 becomes large). They b-^ decay to new elements, which are more stable and capable of capturing more neutrons. This process reaches a limit when nuclei beyond Z = 90 are reached. These nuclei fission into several lighter fragments. The r- process is thought to have a duration of 1 to 100 sec during the peak of the supernova explosion. Fig- ure 3.7 illustrates this process.
Fe + g Æ 13
He + 4
n;
He + g Æ 2
H + 2
n
Lecture 3 Spring 2003
Note that there is no reason why the r-process should lead to different abundances of stable odd and even nuclides. During the r-process, temperatures are so high that capture cross section of odd- and even-mass nuclides are similar and the neutron density is so great that all nuclei will likely cap- ture a number of neutrons. And in the extreme temperatures, all nuclei are in excited states, and rela- tively little systematic difference is expected in the capture cross-sections of odd and even nuclei. That the r-process occurs in supernovae is confirmed by the observation of g-rays from short-lived radionuclides.
The p-process
The r-process tends to form the heavier isotopes of a given element. The p-process (proton capture) also operates in supernovae and is responsible for the lightest isotopes of a given element. The proba- bility of proton capture is much less likely than neutron capture. The reason should be obvious. To be captured the proton must have sufficient energy to overcome the coulomb repulsion and approach to within 10 -13^ cm of the nucleus where the strong nuclear force dominates over the electromagnetic one. Since the neutron is uncharged, there is no coulomb repulsion and even low energy neutron can be cap- tured. As a result, light, p-process only isotopes tend to be the least abundant. Figure 3.8 illustrates how the s- r- and p-processes create different nuclei. Note also the shielding effect. If a given isotope with z protons and n neutrons, a stable neighbor exists with n+x neutrons and p-x protons, this isotope is shielded from production by the r-process. The most abundant isotopes will be those created by all processes; the least abundant will be those created by only one, particu- larly by only the p-process.
p only
p only
r only
r only^ r only
r only
s only
s only s only
s only
s, r
s, r s, r
s, r
s, r
s, r
s, r s, r
b–
decay
N
Neutron-rich matter
Z
Figure 3.8. Z vs. N diagram showing production of isotopes by the r- s- and processes. Squares are stable nuclei; wavy lines are beta-decay path of neutron- rich isotopes produced by the r-process; solid line through stable isotopes shows the s-process path.
Lecture 3 Spring 2003
REFERENCES AND
SUGGESTIONS FOR
FURTHER READING
Burbidge, E. M., G. R. Burbidge, W. A. Fowler, and F. Hoyle.
- Synthesis of the elements in stars, Rev. Mod. Phys. , 29: 547-650. Cowley, C. R. 1995. Cosmochemistry. Cambridge: Cambridge University Press. Prantzos, N., E. Vangioni-Flam and M. Cassé (ed.), 1993, Origin and Evolution of the Elements , Cambridge: Cambridge University Press. Rolfs, C. E. and W. S. Rodney.
- Cauldrons in the Cosmos. Chicago: Chicago University Press. Wasserburg, G. J., M. Busso, R. Gallino and C. M. Raiteri. 1994. Asymptotic giant branch stars as a source of short-lived radioactive nuclei in the solar nebula. Astrophys. J. 424: 412-428. Figure 3.10. Comparison of relative abundances in cosmic rays and the solar system.
Ta
Hf
Lu
Yb
Tm
Er
9 d 8 h
31 d 4 d
6d
70 d
Z
N
129 d 1.9 y 63 h
Figure 3.11. View of Part of Chart of the Nuclides. Mass numbers of stable nuclides are shown in bold, their isotopic abundance is shown in italics as percent. Mass numbers of short-lived nuclides are shown in plain text with their half-lives also given.
